Conditions for convexity of the isotropic function of the second-rank tensor
Vladimir M. Sadovskii
Institute of Computational Modelling, Siberian Branch of the Russian Academy of Sciences, Krasnoyarsk, Russia
For a scalar function, depending on the invariants of the second-rank tensor, condition of convexity and strong convexity are obtained with respect to the components of this tensor in an arbitrary Cartesian coordinate system. It is shown that if a function depends only on the four invariants: three principal values of the symmetric part of a tensor and modulus of pseudovector of the antisymmetric part, these conditions are necessary and sufficient. A special system of convex invariants is suggested to construct potentials for the stresses and strains in the mechanics of structurally inhomogeneous elastic media, exhibiting moment properties.
isotropic tensor function, convexity, invariants, nonlinear elasticity, plasticity.
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Received in revised form: 25.10.2010
Vladimir M. Sadovskii, “Conditions for convexity of the isotropic function of the second-rank tensor”, J. Sib. Fed. Univ. Math. Phys., 4:2 (2011), 265–272
Citation in format AMSBIB
\paper Conditions for convexity of the isotropic function of the second-rank tensor
\jour J. Sib. Fed. Univ. Math. Phys.
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